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Efficiency, Equality, Poverty
Doctoral Course, Université de la Méditerranée – 2008-2009
Nicolas Gravel
« The importance of the formal results lies ultimately in their relevance to normal communication, and to things that people argue about and fight for »
Amartya K. Sen
What are the things that people argue about and fight for ?
People argue about and fight for the defense of their private interest (much too often perhaps)
People argue about and fight for the construction of a « better » world
A better world = a world with less suffering, less exploitation, more…justice
What are the things that people argue about and fight for ?
People argue about and fight for the defense of their private interest (much too often perhaps)
People argue about and fight for the construction of a « better » world
A better world = a world with less suffering, less exploitation, more…justice
What are the things that people argue about and fight for ?
People argue about and fight for the defense of their private interest (much too often perhaps)
People argue about and fight for the construction of a « better » world
A better world = a world with less suffering, less exploitation, more…justice
What are the things that people argue about and fight for ?
People argue about and fight for the defense of their private interest (much too often perhaps)
People argue about and fight for the construction of a « better » world
A better world = a world with less suffering, less exploitation, more…justice
What are the things that people argue about and fight for ?
People argue about and fight for the defense of their private interest (much too often perhaps)
People argue about and fight for the construction of a « better » world
A better world = a world with less suffering, less exploitation, more…justice
« Justice is the first virtue of social institutions, as truth is of systems of thought. A theory however elegant and economical must be rejected or revised if it is untrue; likewise laws and institutions no matter how efficient and well-arranged must be reformed or abolished if they are unjust. »
John Rawls
But what is justice ?
When can we say that a particular social arrangement is « just » and another « unjust » ?
When can we say that a social institution is more just than another ?
Purpose of the course
To present answers proposed by economists to questions
More specifically, to present methods used by economists to compare societies on the basis of their performance in achieving justice
Many methods discussed here are ethically robust
Comparing societies ?
Comparing two different societies at a given moment (is France more just than the US ?)
Comparing a given society at different points of time (is India better now than fifteen years ago ?)
Comparing a society after a tax reform with the same society without the tax reform
etc.
Comparing societies ?
Society = A list of individuals Approaches focus on specific attributes
of these individuals Attributes: Income, health, education,
access to public good, etc. Comparing societies amount to
comparing distributions of these attributes across individuals
Robust methods of normative appraisal ?
Method: we want it to be routinely and « easily » implementable
Based on explicit ethical principles Robustness: ethical principles that justify
the methods are widely acceptable Price to pay for robustness:
Incompleteness. The methods may fail to provide answers to the questions above. Ethical principles may conflict.
Comparing societies: some examples
Comparing 12 OECD countries (+ India) based on their distribution of disposable income and some public goods (based on Gravel, Moyes and Tarroux (2008)
Sample of some 20 000 households in each country (1998-2002)
Disposable income: income available after all taxes and social security contributions have been paid and all transfers payment have been received
Incomes are made comparable across households by equivalence scale adjustment
Incomes are made comparable across countries by adjusting for purchasing power differences
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sweden
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India
What are these data saying on justice ?
Except for the 10% poorest, americans in every income group have larger income than French, swedish and German. Does that mean that US is a « better » society than UK, France, or Sweden ?
Americans in every income group have larger income than British, Australians, Italians, spanish and Indians. Does that mean that US is a better society than UK, Australia, Italy, Spain or India ?
It would seem so if income was the only relevant attribute. But is that so ?
Another attribute: regional infant mortality
Infant mortality (number of children who die before the age of one per thousand births) is a good indicator of the overall working of the medical system of the region where individuals live
How do countries compare in terms of the different infant mortality rate that they offer to their citizens on the basis of their place of residence ?
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France
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Italy
Spain
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India
Other attribute: average class size in public schools
How do countries compare in terms of the distribution of the class sizes at public school ?
Class size: a good indicator of the school quality
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Groups of Class size
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France
Germany
Italy
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General principles that can be derived from these comparisons Countries differ by the total amount of each
attribute they allocate to their citizens :« size of the cake »
They also differ by the way they share this cake
Less obviously, they also differ by the way they correlate the attribute between people (are individuals who are « rich » in income also those who are « rich » in health, or education? )
2 cakes of different sizes: US & Sweden
US
Sweden
Sharing the US cake
2% 4%5%
6%
8%
9%
10%12%
15%
29%
Sharing the Swedish cake
4%6%
7%
8%
9%
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11%12%
14%
19%
Ethical principles examined in this course consider that: For a given distribution, a larger cake is
better than a smaller one Given the size, a « more equal »
distribution of the cake is better than a less equal one (requires a definition of what is meant by « more equal »)
Given sizes and distributions of several « cakes », less correlation between cakes is better
Modern theory of economic justice
A difficult birth: An impossibility theorem (Arrow 1951)
It is impossible to define a consistent and informationally parcimonious ranking of societies that is respectful of individual preferences
Escape out of this theorem have taken two routes: welfarist and non-welfarist
What is justice ? A welfarist answer (1) Welfarism: The only thing that matters for
evaluating a society is the distribution of welfare – happiness - between individuals
Individual preferences are important insofar as they are connected to individual welfare
A just society is a society that maximises an increasing function of individual happiness
Philosophical foundations: Hume, Bentham, Beccaria
What is justice ? A welfarist answer (2)
Fundamental assumption: individual happiness can be measured and compared (necessary to escape from Arrow’s theorem)
We don’t need to know how to measure happiness but we have to accept the idea that we can measure it in a meaningful way.
Individual welfare is assumed to depend upon the individual attributes
The relationship between welfare and attributes is assumed to satisfy basic properties
Specifically, we assume:
Happiness is increasing with respect to each attribute (more income makes people happier, so does more health, smaller class sizes, etc.)
The extra pleasure brought about by an extra unit of an attribute decreases with the level of the attribute (a rich individual gets less extra pleasure from an extra euro than does an otherwise identical poorer individual)
The rate of increase in happiness with respect to a particular attribute is decreasing with respect to every other attribute
Which function of individual happiness should we maximize ?
Classical Utilitarianism (Bentham): the sum Modern view point: a function that exhibits
some aversion with respect to happiness-inequality
Extreme form of aversion toward happiness-inequality (John Rawls): Maxi-Min, we should focus only on the welfare of the less happy person in the society.
Contrasting Maxi-min and Utilitarianism
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Contrasting Maxi-min and Utilitarianism
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Contrasting Maxi-min and Utilitarianism
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sum of income is larger in USthan in UK and in UK than inFrance
Contrasting Maxi-min and Utilitarianism
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sum of income is larger in USthan in UK and in UK than inFrance but the poorest individualis richer in France than in the USor in the UK
To sum up, for welfarism:
1: A society = a list of combinations of observable attributes (one such combination for every individual)
2: Each combination of attributes is transformed into (unobservable) happiness
3: Societies are compared on the basis of their distributions of happiness
Society A is better than society B if the distribution of happiness in A is considered better than that in B by any function that exhibits aversion to happiness-inequality, under the assumption that the relationship between unobservable individual happiness and obervable individual attributes satisfies the above properties (Welfarist dominance)
non-welfarist principles
Some philosophers and economists object to welfarism
They claim that individual happiness is not the only thing that matters, that individual happiness can not be meaningfully measured, and/or that it is not society’s business to be concerned with individual’s happiness
Other individual attributes are considered intrinsically important: freedom, ressources, preferences,…
Object of the course Propose operational methods for comparing societies that
are tightly connected to ethical principles (welfarist or not) Because of the difficulty of accepting a specific ethical
theory, look for methods that are agreed upon by a wide spectrum of ethical theories (robustness)
To the extent possible, try to connect the rankings of societies to elementary operations having a clear meaning
Theory of this is well-established when attention is restricted to distributions of one attribute (income)
A lot of research is needed to develop robust methods for the multi-attributes case
When can we say that one society is better than another ? (the one attribute case)
n individuals identical in every respect other than the considered attribute (income)
y = (y1,…,yn) an income distribution
y(.) = (y(1),…,y(n)) the ordered permutation of y (considered equivalent to y if the ethics used is « anonymous »)
Q: When are we « sure » that y is « more just » than z ?
Anwer no 1: Mana and Robin Hood
When y(.) has been obtained from z(.) by giving mana to some, or all, the individuals
When y(.) has been obtained from z(.) by a finite sequence of bilateral Pigou-Dalton (Robin Hood) transfers between a donator that is richer than the recipient.
When y(.) has been obtained from z(.) by both manas and Robin Hood transfers
Mana ?
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Mana ?
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Answer no 2: Poverty dominance
Important issue: poverty How do we define poverty ? Basic principle: You define a (poverty)
line that partitions the population into 2 groups: poor and rich
2 measures of poverty
1) Headcount: Count the number (or the fraction) of people below the line
2) poverty gap: Calculate the minimal amount of money needed to eliminate poverty as defined by the line
Contrasting headcount and poverty gap
Australia Austria Canada France Germany Italy Portugal Spain sweden Switz. UK USA India
4733 6815 4285 6170 5855 3554 2546 2747 5808 8679 4898 5403 789
9237 10730 8977 9555 10012 6575 4602 5407 9056 14615 8598 11025 1019
11795 12850 11935 11793 12024 8059 6110 7045 10540 17334 10883 14687 1168
14580 14725 14338 13441 13229 9438 7549 8646 11982 19806 13337 18142 1309
17377 16588 16839 15092 14857 10933 8666 10113 13371 22044 15854 21581 1462
20456 18665 19494 16966 16614 12629 10028 11656 14723 24554 18579 25206 1649
24203 20921 22382 19169 18376 14769 11415 13639 16147 27696 21574 29387 1859
28467 24042 25955 22382 21221 17342 13930 16535 18140 32095 25188 34819 2167
34592 28069 30958 26834 25201 20743 18113 20968 21091 38254 30190 43373 2694
54537 38539 44457 40175 39217 31174 32047 35457 30818 61849 49022 79030 4735
Line = 9 600
There are 2 poor in France and 1 poor in germanybut poverty gap in Germany is 3745 while it is only3465 in France
Poverty dominance Problem with poverty measurement: how
do we draw the line ? Criterion: society A is better than society
B if, no matter how the line is drawn, poverty is lower in A than in B for the poverty gap (poverty gap dominance)
Answer no 3: Lorenz dominance Lorenz dominance criterion: Society A
is better than society B if the total income held by individuals below a certain rank is higher in A than in B no matter what the rank is.
Easy to see with Lorenz curves. Let us draw Lorenz curves with our data.
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Cool! the 3 answers are all equivalent to the welfarist dominance answer
It is equivalent to say : society A is more just than society B for any
welfarist ethics One can go from B to A by a finite sequence
of Robin Hood transfers and/or mana Poverty gap in A is lower than in B for all
poverty lines Lorenz curve in A is everywhere above that
in B.
This result is a beautiful one
Comes from mathematics: Hardy, Littlewood & Polya (1936), Berge (1959),
Adapted to economics by Kolm (1966;1969), Dasgupta, Sen and Starett (1973) and Sen (1973)
It provides a solid justification for the use of Lorenz curves
Lorenz dominance chart
Switzerland US
UKAustralia
Canada
Austria
France Germany
Sweden
Italy
Spain
Portugal
India
Important challenge: to extend to many attributes
Same welfarist ethics Suitable generalization of poverty notions
(poverty in several dimensions) No Lorenz curves New issue: Correlation between
attributes
Aversion to correlation ?
Literacy rate (%)
Income (rupees/month)400 700
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6050
600
a red society
Aversion to correlation ?
Literacy rate (%)
Income (rupees/month)400 700
40
70
500
6050
600
a red society
and a white society
Aversion to correlation ?
Literacy rate (%)
Income (rupees/month)400 700
40
70
500
6050
600
a red society
and a white society
white society is more just
Bidimensional dominance chart
Switzerland
USUKAustralia Canada Austria
FranceGermany Sweden
Italy
Spain
Portugal
India